WASHINGTON — After the shooting of Rep. Gabrielle Giffords of Arizona and others in early 2011, the Justice Department drew up a detailed list of steps the government could take to expand the background-check system to reduce the risk of guns falling into the hands of mentally ill people and criminals.

The proposals, though, were shelved at the department without action against the backdrop of the election campaign and the politically charged congressional investigation into the Operation Fast and Furious gun trafficking case, according to people familiar with the internal deliberations.

Although it is not clear whether any of the proposals would have had an effect on the massacre Friday at an Connecticut elementary school, the set of recommendations could provide a blueprint if the Obama administration chooses to go forward with more aggressive steps to curb gun violence.

The Justice Department’s list included several measures that President Barack Obama could enact by executive order even if Congress failed to take any new actions.

In brief remarks Friday, Obama said, “We’re going to have to come together and take meaningful action to prevent more tragedies like this, regardless of the politics.”

But it is not clear whether the White House has the political will to follow through on that call against the powerful gun-rights lobby and amid competing concerns, like negotiations over the looming fiscal deadline and debt ceiling issues.

The Justice Department’s study centered on ways to bolster the database the FBI uses to run background checks on gun purchasers with information already in the hands of other federal agencies. Certain categories of people are barred from buying guns, including felons, drug users, people adjudicated to be mentally “defective,” illegal immigrants and people under court orders or convicted of misdemeanor offenses related to domestic violence.

For example, the department study recommended that Obama order all agencies that give out benefits — like the Social Security Administration — tell the FBI background-check system whenever they have made arrangements to send a check to a trustee because the recipient is mentally incompetent, or when federal employees or job applicants fail a drug test.

The officials also recommended setting up a system to appeal such determinations if, for example, people say their mental health has improved. While such steps could raise privacy concerns, they conducted a legal analysis and concluded it was appropriate.

The list also proposed congressional action, including increasing financing to states as an incentive to submit their own law enforcement information to the database, expanding the transactions subject to background checks and increasing penalties on people who act as “straw” buyers to help people obtain weapons who would have been blocked by a background check.

White House and Justice Department officials did not respond to requests for comment about their plans or the Justice Department’s earlier project, the details of which were described to The New York Times by people familiar with it. While the recommendations were discussed a year ago with senior department officials, including Attorney General Eric Holder and his deputy, James Cole, it is not clear whether they ever reached the White House.

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